Electron Scattering - Startseite...A Practical Theory Course Vsevolod V. Balashov, Alexei N....

Electron ScatteringFrom Atoms, Molecules, Nuclei,and Bulk Matter

Edited by

Colm T. WhelanOld Dominion UniversityNorfolk, Virginia

and

Nigel J. MasonUniversity College LondonLondon, England

Kluwer Academic/Plenum PublishersNew York, Boston, Dordrecht, London, Moscow

Library of Congress Cataloging-in-Publication Data

Electron scattering: from atoms, molecules, nuclei, and bulk matter/[edited by] Colm T.Whelan, Nigel J. Mason.

p. cm. — (Physics of atoms and molecules)Includes bibliographical references and index.ISBN 0-306-48701-2 — ISBN 0-306-48702-0 (eBook)

1. Electrons—Scattering—Congresses. 2. Chemistry, Physical andtheoretical—Congresses. I. Whelan, Colm T. II. Mason, Nigel J. (Nigel John) III. Series.

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2004054593

ISBN 0-306-48701-2

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Electron ScatteringFrom Atoms, Molecules, Nuclei,and Bulk Matter

PHYSICS OF ATOMS AND MOLECULESSeries Editors

P. G. Burke, The Queen's University of Belfast, Northern Ireland

H. Kleinpoppen, Atomic Physics Laboratory, University of Stirling, Scotland

Editorial Advisory Board

R. B. Bernstein (New York, USA.) W. E. Lamb, Jr. (Tucson, USA.)

J. C. Cohen-Tannoudji (Paris, France) P.-O. Lowdin (Gainesville, USA)R. W. Crompton (Canberra, Australia) H. O. Lutz (Bielefeld, Germany)Y. N. Demkov, (St. Petersburg, Russia) M. C. Standage (Brisbane, Australia)C. J. Joachain (Brussels, Belgium) K. Takayanagi (Tokyo, Japan)

Recent volumes in this series:

COMPLETE SCATTERING EXPERIMENTSEdited by Uwe Becker and Albert Crowe

ELECTRON MOMENTUM SPECTROSCOPYErich Weigold and Ian McCarthy

ELECTRON SCATTERINGFrom Atoms, Molecules, Nuclei, and Bulk MatterColm T. Whelan and Nigel J. Mason

FUNDAMENTAL ELECTRON INTERACTIONS WITH PLASMA PROCESSINGGASESLoucas G. Christophorou and James K. Olthoff

IMPACT SPECTROPOLARIMETRIC SENSINGS. A. Kazantsev, A. G. Petrashen, and N. M. Firstova

INTRODUCTION TO THE THEORY OF COLLISIONS OF ELECTRONS WITHATOMS AND MOLECULESS. P. Khare

NEW DIRECTIONS IN ATOMIC PHYSICSEdited by Colm T. Whelan, R. M. Dreizler, J. H. Macek, and H. R. J. Walters

POLARIZATION AND CORRELATION PHENOMENA IN ATOMIC COLLISIONSA Practical Theory CourseVsevolod V. Balashov, Alexei N. Grum-Grzhimailo, and Nikolai M. Kabachnik

RELATIVISTIC HEAVY-PARTICLE COLLISION THEORYDerrick S. F. Crothers

A Chronological Listing of Volumes in this series appears at the back of this volume.

A Continuation Order Plan is available for this series. A continuation order will bring delivery of eachnew volume immediately upon publication. Volumes are billed only upon actual shipment. For furtherinformation please contact the publisher.

CONTENTS

Atomic Confinement 1Jean-Patrick Connerade and Prasert Kengkan

Correlation Studies of Two Active-Atomic-Electron Ionization Processes inFree Atoms *13Albert Crowe and Mevult Dogan

Coherent Electron Impact Excitation of Atoms 23Danica Cvejanovi£, Albert Crowe and Derek Brown

Electron and Photon Impact Studies of CF3I ..... 33S Eden, P Lintio Vieira, N J Mason, M Kitajima, M Okamoto, H Tanaka, DNewnham and S Hoffmann

Time Delays and Cold Collisions 45D Field, N C Jones and J-P Ziesel

Relativistic Basis Set Methods 55Ian P Grant

Inner Shell Electron Impact Ionization of Multi-Charged Ions 69Marco Kampp, Colm T Whelan and H R J Walters

A Study of Iterative Methods for Integro-DifferentiaJ Equations ofElectron —Atom Scattering ........*...»•*•.*......•••........•......... 77Satoyuki Kawano, J Rasch, Peter J P Roche and Colm T Whelan

Relaxation by Collisions with Hydrogen Atoms: Polarization of SpectralLines ••••••••• 87Boutheina Kerenki

Electron Energy Loss Spectroscopy of Trifluromethyl SulpherPentaflouride........................................................ 99P A Kendall and N J Mason

The Use of the Magnetic Angle Charger in Electron Spectroscopy I l lGCKing

Mechanism of Photo Double Ionization of Helium by 530 eV Photons 121A Knapp et al

Exchange Effects in the Outer Shell Ionization of Xenon 131U Lechner, S Keller, E Engel, H Ludde and R M Dreizler

Ionization of Atoms by Anti-Proton Impact 143J H Macek

High Resolution Electron Interaction Studies with Atoms, Molecules,Biomolecules and Clusters 149G Hanel et al

Electron-Driven Proceeses: Scientific Challenges and TechnologicalOpportunities • 179Nigel J Mason

Quantum Time Entanglement of Electrons.......... 191J H McGuire and A L Godunov

Analytic Continuation: Continuum Distorted Waves 209M Me Sherry, DSF Crothers and SFC O'Rourke

Electron Impact Ionization of Atoms with Two Active Target Electrons ... 217Pascale J Marchalant, Colm T Whelan and H R J Walters

Electron Collisions with Aggregated Matter 225J B A Mitchell

Rotational and Vibrational Excitation in Electron Molecule Scattering 235RKNesbet

Interactions between Electrons and Highly Charged Iron Ions 255B E O'Rourke, F J Currell and H Watanabe

An Investigation of the Two Outermost Orbitals of Glyoxal and Biacetyl byElectron Momentum Spectroscopy.................................................................. 265Masahiko Takahashi, Taku Saito and Yasuo Udagawa

Electron Scattering from Nuclei 279J W van Orden

Electron Scattering and Hydrodynamic Effects in Ionized Gases . ..... 291L Vuskovic and S Popovic

Testing the Limits of the Single Particle Model in 16O(e,e',p) 301L B Weinstein et al

(y,2e) and (e^e) using a 2-Electron R operator Formalism 313Peter J P Roche, R K Nesbet and Colm T Whelan

Laboratory Synthesis of Astrophysical Molecules: a New UCL Apparatus.... 329Anita Dawes, Nigel J Mason, Petra Tegede, Philip Holtom

Preface

There is a unity to physics; it is a discipline which provides the most fundamental understanding of the dynamics of matter and energy. To understand anything about a physical system you have to interact with it and one of the best ways to learn something is to use electrons as probes. This book is the result of a meeting, which took place in Magdalene College Cambridge in December 2001. Atomic, nuclear, cluster, soHd state, chemical and even bio- physicists got together to consider scattering electrons to explore matter in all its forms. Theory and experiment were represented in about equal measure. It was meeting marked by the most lively of discussions and the free exchange of ideas. We all learnt a lot.

The Editors are grateful to EPSRC through its Collaborative Computational Project program (CCP2), lOPP, the Division of Atomic, Molecular, Optical and Plasma Physics (DAMOPP) and the Atomic Molecular Interactions group (AMIG) of the Institute of Physics for financial support. The smooth running of the meeting was enormously facilitated by the efficiency and helpfulness of the staff of Magdalene College, for which we are extremely grateful. This meeting marked the end for one of us (CTW) of a ten-year period as a fellow of the College and he would like to take this opportunity to thank the fellows and staff for the privilege of working with them.

Colm T Whelan Nigel John Mason Department of Physics Department of Physics and Astronomy OLD Dominion University The Open University Norfolk Walton Hall Virginia Milton Keynes 23529 MK7 6AA USA UK

ATOMIC CONFINEMENT

Jean-Patrick ConneradeQuantum Optics and Laser Science Group, Physics Department, Imperial College

London SW7 2BW UK

jxonneradeOic.ac.uk

Prasert KengkanPhysics Department, University of Khon Kaen

Khon Kaen 40002 Thailand

prasert kQkku.act h

Abstract We review the recent revival of interest in the subject of confined atoms,motivated by experimental developments in a number of areas, e.g.atoms under extreme pressure, atoms confined in zeolites, in bubbles, insolids, in quantum dots or trapped in molecular cages, as occurs in met-allofullerenes. The subject originated very early in the development ofquantum mechanics, and even provided a theme for Arnold Sommerfeldin a birthday celebration in honour of Wolfgang Pauli. After this highpoint, it languished relatively unnoticed, except by a few practitionerswho mostly used wavefunctions of confined atoms as a starting approx-imation to describe atoms in solids. The recent discovery of new formsof confinement demonstrates that concepts must be refined to bring outthe rich diversity of effects expected in the spectroscopy of confinedatoms. They allow atomic behaviour to be explored under novel cir-cumstances, and provide a new bidge (alternative to cluster physics)from the atom to the solid. At present, metallofuilerene targets are stilldifficult to manufacture with sufficient number density for ultravioletand soft X-ray spectra to be probed. It is likely that this experimentalproblem will soon be resolved. Thus, the motivation already exists topredict what novel effects may occur and what their likely spectral man-ifestations will be. This should turn into a thriving new area.. Somecurrent theoretical problems in the treatment of confined atoms will bedescribed. A discussion of the recent classification of resonances in con-fined atoms into three different types will e presented. The influence ofconfinement on correlations will be indicated. Possible connections tothe theory of EXAFS will be outlined.

Keywords: confined atoms, clusters, quantum dots, fullerenes. metallofullerenes

2 Jean-Patrick Connerade and Prasert Kengkan

IntroductionIn addition to the fact that they involve new objects - for example, the

metallofullerenes, quantum bubbles or quantum dots - whose existencehad not previously been supposed, confined atoms are of interest for a va-riety of reasons. First, they offer prospects of a new path in the practicalapplication of atomic physics. Second, they complete our understandingof classical problems in atomic physics, such as the self-consistent field orquantum defect theory, where new boundary conditions can be applied.Third, they offer the possibility of allowing correlations to be activelyprobed, both experimentally and theoretically.

Thus, the confined atom emerges as a new and distinctive topic inatomic physics. Like any new problem it has its own history, and thismust first be described, to dispell the impression that it has suddenlycome out of the blue. In this sense, it is similar to the subject of clusterphysics, which also emerged in recent times as an apparently new devel-opment, but actually has its roots in early experiments, especially thestudy of atomic beams for Stern-Gerlach measurements. The parallelwith cluster physics is an interesting one. As we shall bring out, thereare also interesting differences between these two subjects, which havein some ways developed along opposite lines.

In the present paper, we review some of the early history of confinedatoms, then present some more recent work, culminating in actual ex-perimental realisations. In conclusion, we present our own view as tothe importance of this area of atomic physics, and the reasons why itdeserves to be pursued.

1. Some Early HistoryIn contrast to cluster physics, which has a long history of having been

missed by the early investigators of the Stern-Gerlach effect who consid-ered clusters as some kind of molecular nuisance, confined atoms werediscovered early, and, for a long time, investigated only as theoretical ob-jects, with some esoteric applications. The earlest relevant paper seemsto be the one of Michels et al. [1], who were concerned about the effectsof very high pressures. They suggested to replace the interaction of theatoms with surrounding atoms by a uniform pressure on a sphere withinwhich the atom is considered to be en closed. This led them to considerthe problem of hydrogen with modified external boundary conditions.This paper was soon followed by a very remarkable contribution to thesubject, due to Sommerfeld and Welker [2]. These authors realised thatone could actually solve the confined hydrogen problem exactly, becausethe existing excited state solutions for higher ns functions of the free

Atomic Confinement 3

hydrogen atom satisfy the modified boundary conditions exactly for cer-tain combinations of n and the cavity radius, when a node occurs at thecavity wall.

From the early studies of Sommerfeld and Welker [2], the general lawof energy variation with of the ground state binding energy with cav-ity radius for hydrogen was obtained, and certain rules were establishedconcerning the degree of binding which turn out to be general for allatoms in cavities. In particular, they showed that there exists a cavityradius below which the optical electron is no longer bound. Sometimes(following [2], this is described as 'ionisation' but a better word is per-haps delocalisation, since the electron is no longer bound to the atom,but is still confined within the cavity). They applied their analysis tothe new situation of an atom confined within the Wigner-Seitz cell in asolid, and argued that, below this critical radius, the situation resemblesthe formation of the conduction band.

Although it is not usually thought of in this way, one can also re-gard the Thomas-Fermi model of the atom as an example of quantumconfinement, since it imposes a finite radius, outside which there is noelectronic charge density. Thus, in a sense, all the more refined meth-ods which stem from Density Functional theory, such as the LDA, areexamples of atomic confinement, which may also explain why they areso effective to describe the behaviour of atoms in solids.

Thus, spherical confinement emerged essentially as a theoretical prob-lem, brought about by the desire to transfer separability and the conven-tional structure of atomic physics to confined species, rather than as anexperimental discovery. This is the opposite situation to the discoveryof clusters, where studies of optical absorption in metallic vapours or ofthe Stern-Gerlach effect in atomic beams both indicated the presence ofnew types of molecules. In the case of metallic clusters, the assumptionof spherical symmetry was also introduced in, say, the jellium model,but this came in later, to aid in the interpretation of the results.

2. Modern DevelopmentsThe more recent papers on confined atoms relate rather to the excite-

ment generated by the discovery of new objects such as metallofullerenes,in which an atom is trapped within what is an almost spherical molec-ular 'cage'. This has led to a revival in the physics of confined atoms,and to widespread interest in the spectroscopy of such species.

Again, the predominant theoretical approach is to assume that spher-ical symmetry applies, and to modify the external boundary conditionsappropriately. Note that, even for Ceo the true boundary conditions are


not spherical. In quantum mechanics, a perfect sphere cannot rotate, sothere are features of the true physical problem which disappear underthe assumption of spherical symmetry, most notably rotation and vi-bration of the confining cavity. Nonetheless, a variety of simple modelshave been developed and applied, to represent not only hydrogen, butalso many-electron atoms in cavities. Regarding the boundary condi-tions, the scope has also widened. It now extends to penetrable as wellas impenetrable spheres, and to potentials which can be attractive aswell as repulsive, with soft or hard edges.

Symptomatic of the more modern approach is the work of Boeyens [3],who modelled atomic compression in Hartree-Fock-Slater numerical cal-culations by changing the outer boundary conditions, and calculated thecritical radius ro for many-electron atoms. These ionisation radii' (touse his term) were found to exhibit a remarkable periodicity, commen-surate with the known chemistry of the elements, and could thereforebe regarded as a new fundamental theoretical index chemical activity.

In the work of Boeyens [3], it was assumed that the chemical responseof an atom is somehow governed by the ease with which it can be ionisedby compression, but chemical activity is often an elusive concept, andthe physics of this 'chemical pressure' was not explored. In fact, thebehaviour of compressed many-electron atoms is highly non-linear [4].In a series of papers [5, 6, 7] Connerade argued that atomic compress-ibility is intimately linked to the theory of orbital collapse [8, 9] andis indeed related to the idea of controlled collapse [10, 11]. Thus, themost interesting cases for study (the 'softest' atoms) are those in whichthe order of filling of the shell structure can be altered under pressure[12] so that the Periodic Table under pressure (and, by implicaton: thechemistry) becomes different from that for free atoms.

3. Dimensionless Plots of CompressibilityThe property of non-linearity rendered the representation of the data

and the comparison between different atoms somewhat unclear untila method of dimensionless representation applicable to all atoms wasproposed [13]. It was then found that the atomic compressibility (anessentially coulombic property), when reduced to these dimensionlessvariables, becomes nearly the same for all atoms, essentially because ofthe scalability of coulomb forces. Once this nonlinear part is accountedfor, what remains is an atomic factor independent of pressure, which isa hardness characteristic of each atom in the ground state.

Let the mean volume occupied by the free atom V* = 4TT < r3 >/3 , where < r3 > is the expectation value of r3, calculated from the


outermost wavefunction of the atom. Then, the corresponding quantityVp can again be defined for the atom under a pressure p, arising fromany kind of spherical potential, as explained above. We introduce thedimensionless shrinkage parameter

Z = Vp/Vf (1)

From the definitions, we can deduce that the quantum pressure

P =AEAV

e - lyj - -

P=VP(2)

where p is a reduced pressure. What our definitions of e and £ achieveis to scale all the variables systematically by the appropriate factor foreach atom, yielding a reduced compressibility. The important point, aswe will show, is that most of the variation of compressibility from atomto atom is removed by this method of scaling, so that, for all atoms, theactual variation in s as a function of £ turns out to be almost the same.

2.4

Figure 1. Dimensionless plot of compressibility (see text)

Some indication of how this occurs comes from magnitudes obtainedfor free atoms. From multiconfigurational Dirac-Fock calculations, wefind, for caesium:

zEes/7r < r6s >3 = 1.3591 * 1(T4 a.u.~2


while, for helium:rjHe = jEu/n < rls >3 = 0.27491 a.u."2,

which implies that Cs (one of the largest atoms in the Periodic Table)is roughly 2000 times more compressible than He (the smallest atom),provided e and £ exhibit similar variations.

Since both e and £ are dimensionless, we can now plot the reducedcompressibility, or (£,£) curves for all atoms onto a single graph.

From the data used to plot the confined atom curves, we can alsodeduce the reduced quantum pressure p by using equation (3) above.This can be plotted against the volume ratio £. The interesting feature ofsuch a plot is that, again, there is a marked similarity between the curves,despite an enormous difference of hardness between the two atoms. Withappropriate scaling, even the functional variations turn out to be nearlythe same over a wide range.

We now enumerate some general features of (s,£) curves:

(i) As the spherical perturbation tends to zero (for example the heightof the confining step V 4£ 0, or the nuclear charge tends to that of theneutral atom) then both e = 1 and $ = 1, so that all the (e,£) curvesgo through a universal point (1,1).

(ii) Since a free neutral atom exists only at zero pressure, and since zeropressure corresponds to de/d£ = 0, it follows that the slope of the (e,£)for the neutral atom confined by a sphere tends to zero as (e,£)—>(1,1).(iii) For atoms compressed by an impenetrable repulsive sphere, thereis a confining radius within which EP

B, and therefore also e, changessign, i.e. the (e,£) curve crosses the e = 0 abscissa. This correspondsto delocalisation,

(iv) For atoms compressed by an increase in nuclear charge, the ionisa-tion potential increases with charge, i.e. as the atom becomes smaller,its binding energy also increases, so the (e, f) curves veer upwards ratherthan downwards.

(v) Atoms can be dilated as well as compressed by a spherical perturba-tion, either by a reduction of nuclear charge or by an attractive sphericalshell. In this case, the binding energy is reduced, until eventually ioni-sation occurs. Since an increase in ionisation potential never occurs ondilation, there is a forbidden region for £ > 1, e > 1 in the (e,f) plane.

(vi) The real physical pressure is given by p — rj[(e — l)/(£ — 1)]. Thefirst factor undergoes a very large variation from atom to atom, fromthe smallest atom in the Periodic Table with the highest binding energy,which is He, to the largest atom with the smallest binding energy, i.e.a heavy alkali (Cs or Fr), which define the hardest and softest atomsrespectively.

(vi) Slightly different curves are obtained if compression is applied tothe atom by using an external cavity, or else by the device of a fractionalincrease in nuclear charge, which is sometimes used to generate startingfunctions in applications to solid state physics (internal compression).


The reason for the difference is that increasing thee nuclear charge can-not ionise the atom, whereas external compression eventually results indelocalisation, as explained above

Of course, to describe the filling of shells in transition elements andlanthanides really requires a relativistic model for consistency. Sincethe most interesting cases are the heavy atoms, it became importantto develop a fully relativistic model of the confined atom. This posessome specific and non-trivial problems as regards the implementation ofboundary conditions [14] but at least within reasonable approximationssuch a theory can now be formulated, and has been applied with successto a parameter-free calculation of the isomorphic phase transition in Csmetal [15], with results in quite good agreement with experiment.

4. Boundary Conditions and External PotentialsDevelopments have also taken place in the manner of treating the

boundary conditions and the externally applied potentials. In the workof Sommerfeld and Welker [2], the boundary condition was an infinitelyhigh wall at the radius of the confining cavity, corresponding to an im-penetrable sphere. This is convenient when dealing with hydrogen, sincethe radius of the cavity then corresponds exactly to a node in the wave-function. For other atoms, however, it is not such a useful approximationsince several nodes very rarely coincide. Arguments against it are as fol-lows:

(i) For all cases which must be solved numerically, the infinitely high wallposes computational problems, because a discontinuity is created at theradius of the cavity. It is numerically more stable to pick a fairly highvalue for the height of a finite step, and to verify that the wavefunctiondecays exponentially at radii larger than the radius of the cavity, fallingto a low value within a few points of the mesh. One must also checkthat the binding energy is essentially unchanged by small changes in themagnitude of the step. There are many subtle tricks to achieve reliableconvergence, especially as cavity radii become small.

(ii) An infinitely high step is an unrealistic assumption, because it ef-fectively isolates the atom from the rest of the universe by placing it ina totally impenetrable sphere. To model a real situation, one needs tointroduce a potential of finite depth as the confining cavity, and perhapsalso to consider how abrupt its edges can be.

(iii) Many of the real confinement problems involve specific forms of po-tential barrier. For example, an atom in a solid is usually modeled [16]by confining it within a Watson sphere [17] which gives a more suitableform to the wavefunction at large distances. In metallofullerenes, thepotential is a thin hollow shell, and is attractive. Luckily, making rea-sonable assumptions about its geometry, one can deduce its depth fromthe observed binding energies of fullerene negative ions.


(iv) If one considers the fully relativistic problem, then an infinitelyhigh potential step at a given value ro is, it turns out, an inconsistentboundary condition. The symptom which reveals that it violates thelaws of relativity is that, if imposed, it would lead to what is knownas Klein's paradox, i.e. the spontaneous creation of electron positronpairs, which is clearly unphysical [18].

For all these reasons, a good deal of effort has been expended inimproving and refining the boundary conditions and obtaining suitablepotentials. It is now understood how to select suitable potentials formost problems, and the differences between the relativistic and non-relativist ic conditions are also understood.

5, Beyond the Spherical Cavity and CentredAtom

The simplest model problem concerns the atom at the centre of aspherical confining cavity, because that is the easiest situation to cal-culate. However, it does not correspond to any real physical situation,and one must therefore see it as the starting point in a series of simplemodels or approximations which allow us to understand the behavioureither of real systems or of much more complex and unwieldy numer-ical treatments whose physical content is hard to understand withoutreference to such models.

Several situations arise which can be regarded as a straightforwardstep beyond the simple spherical model, viz:

(i) The atom is not necessarily at the centre of the sphere, but may beoff-centre. In practice, this depends to a large extent on whether thecavity has attractive or repulsive walls. With repulsive walls, the atomtends to be forced to the centre of the cavity [19]. With attractive walls(as in a fullerene) the atom tends to be off-centre, on an orbit withinthe cavity. This problem can be treated perurbatively, by expanding asa sum of spherical harmonics, as a number of authors have shown [20]

(ii) The cavity is not necessarily spherical, but can be a oblate or aprolate spheroid. This tends to happen for some of the fullerenes, whichare closed shells but are not spherical (for example Cg2). This situationcan be modeled by introducing a more elaborate set of coordinates,which allows the cavity to be distorted progressively from its sphericalshape [21]. It is also possible to consider other problems such a sphericalclusters becoming attached to a surface in terms of such coordinates.

(iii) The atom can be inside a cavity which is not a complete sphere,but is made up of scattering points distributed symmetrically over itssurface. This problem has been tackled by Baltenkov et al [22] whointroduced a factorisation to represent these scattering centres, providedthe amplitudes of the atomic functions are small in the vicinity of theconfining 'sphere'. Thi problem is clearly very similar to the treatment


of scattering by a 'coordination sphere' which occurs in the analysis ofEXAFS.

6. Cavity Resonances, and the ExcitationSpectra of Confined Atoms

The confined atom has a clear spectral signature, which can be de-duced from simple calculations, and is confirmed by more elaborate cal-culations. Essentially, it is the excitation spectrum of the atom dressedby the cavity. The cavity itself exhibits characteristic resonances, whichare essentially those of the spherical square well [23]. They can occur inamongst the bound states, in which case they appear as 'anticrossings'or may lie in the continuum, in which case they appear as 'cavity res-onances' which will be seen in the photoionisation spectrum [24], Theextent to which these cavity resonances persist to high energies dependson how completely the surface of the confining shell is covered withelectrical charge.

Thus, the spectrum of a confined atom is a combination of featureswhich would arise for the free atom, but are modified by the presence ofthe cavity, of features which would arise for a cavity, but are modifiedby the presence of an atom inside, and of features which are new, i.e.would not be displayed either by the atom or the cavity in isolation.As an example of the latter, one can take the fact that the true cavityis not perfectly spherical even for Ceo- It therefore breaks the atomicsymmetry, allowing different angular momentum states to mix. As aresult, new excitation channels appear [25] for the confined atom whichwould not be present in the free atom limit. Resonances of this natureare termed 'molecular' because they arise in the same manner as themolecular shape resonances in photoionisation [26].

One can thus achieve a classification of resonances in confined atomsinto three basic types [27]:

(i) Atomic resonances

(ii) Cavity resonances

(iii) Molecular resonances.

Usually, these three types of resonances are well-separated in energy.However, it is also possible that they come together in energy, and ex-hibit features which denote mutual interactions. We have already men-tioned the avoided crossings in the bound state region of the spectrum.In the continuum, autoionising features are found [?] which can exhibitall the properties associated with interacting resonances in conventionalatomic physics [29], Furthermore, by modifying the properties of theconfining shell, which can be achieved by exciting or removing an elec-


tron, one can 'tune' cavity resonances in and out of coincidence withatomic structure, which opens up completely new possibilities

7. CorrelationsThere remains an interesting question, namely the way in which elec-

tron correlations are modified by confinement of the atom inside a cavity.Naively, one might expect that correlations would increase, simply be-cause the electrons are brought closer together. However, this turns outnot to be the case. In fact, correlations may be either increased or de-creased by confinement. In some cases, the energy spacing between shellsincreases on confinement, so that correlations are actually reduced, whilein other cases (especially in the presence of orbital collapse) energy dif-ferent configurations move closer together when the atom is compressed.

Since the issue is a complex one, attempts have been made [28] todevelop general models such as the RPAE and apply them to the confinedatom. At the moment, there exist very few calculations of this type, thecases studied being the smallest atoms in which orbital collapse occurs.However, this is clearly an interesting area for future investigations.

ConclusionAs we have stressed all along, there are a number of new experimental

situations which relate closely to the theory of confined atoms, and whicheither exist already, or are on the point of being realised. For example,the ultraviolet spectroscopy of endohedrally confined atoms (metallo-fullerenes) is not yet achieved, essentially because it is difficult to createthe material in sufficient number density to be probed, but new methodsare being developed for this purpose [30]. Also, bubbles in solids havebeen discovered in the walls of nuclear reactors, which are due to ageing,and the pressure inside them can be deduced from the spectroscopy ofthe atoms they contain [31]. Similarly, the theory of quantum dots em-ploys a Hamiltonian which is essentially the same as that of a confinedatom [32]. More speculatively, one can also consider atoms confinedwithin nanotubes or nanowires, in which the external symmetry will becylindrical rather than spherical, and the consequences this might havefor both shell filling and chemistry.

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[4] J.-P. Connerade 1996 J. of Alloys and Compounds 255 (1-2), 79

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[6] J.-P. Connerade 1983 Journal of the Less Common Metals 93, 171

[7] J.-P. Connerade J. Olivier-Fourcade and J.-C. Jumas 2000 J. Solid State Chem-istry 152, 533

[8] J.-P. Connerade 1978 Contemporary Physics 19, 415

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[12] J.-P. Connerade V.K. Dolmatov and P. Anantha Lakshmi 2000 J. Phys. B: At.Mol. Opt. Phys. 33, 251

[13] J.-P. Connerade P. Kengkan P. Anantha Lakshmi and R. Semaoune 2000 J. Phys.B: At. Mol. Opt. Phys. 33, L847

[14] V. Aionso and S. De Vincenzo 1997 J. Phys. A: Math Gen 30, 8573

[15] J.-P. Connerade and R. Semaoune 2000 J. Phys. B: At. Mol. Opt. Phys. 33, 3467

[16] R. R u u s 1999 Dissertationes Physicae Universitatis Tartuensis 3 1 1

[17] R.E. Watson 1958 Phys. Rev. I l l 1108

[18] A. Calogeracos and N. Dombey 1999 Contemp. Phys. 40 313

[19] V.I. Pupyshev 2000 J. Phys. B: At. Mol. Opt. Phys. 33 961

[20] T.-Y. Shi H.-X. Qiao and B.-W. Li 2000 J. Phys. B: At Mol. Opt Physics 33L349

[21] J.-P. Connerade A.G. Lyalin R. Semaoune and A.V. Solov'yov 2001 J. Phys. B34 2505

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[23] Y.-B. Xu M.-Q. Tan and U. Becker 1996 Phys. Rev. Lett. 76 3538

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[26] D. Dill and J.L. Dehmer 1974 J. Chem. Phys. 61 692

[27] J.-P. Connerade V.K. Dolmatov P.A. Lakshmi and S.T. Manson 1999 J. Phys.B: At. Mol. Opt. Phys. 32, L239

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CORRELATION STUDIES OF TWO ACTIVE-ATOMIC-ELECTRON IONIZATION PROCESSESIN FREE ATOMS

Albert CroweDepartment of PhysicsUniversity of Newcastle, Newcastle upon Tyne, NE1 7RU, [email protected]

Mevlut DoganPhysics DepartmentFaculty of Science, Kocatepe University, Afyon, Turkey

Abstract During the last decade major advances have been made in the modellingof low energy inelastic scattering processes involving a single atomicelectron. Experimental correlation studies of these processes have ex-posed the inadequacies of earlier calculations and played a key role inproviding sensitive tests of the new theoretical approaches. Interest,both experimental and theoretical, is now turning to the more diffi-cult problems involving two active atomic electron processes. The lat-est developments in this area are discussed with emphasis on doubleexcitation-autoionization and simultaneous excitation-ionization.

Keywords: ionization, autoionization, ionization-excitation

IntroductionThe experimental study of the dynamics of inelastic electron scat-

tering from atoms was greatly enhanced by the application of coinci-dence/correlation techniqes to these processes. Two pioneering experi-ments were those of Ehrhardt et al1 for ionization and Eminyan et al2

for excitation. The ionization results from these (e,2e) experiments,expressed as triple differential cross sections (TDCS), showed that theejected electrons were preferentially ejected into two angular regions,referred to as the binary and recoil peaks. The excitation data fromelectron-photon correlation measurements allowed a complete descrip-

13

14 Albert Crowe and Mevlut Dogan

tion of the excitation process, including both the magnitudes and phasesof excitation amplitudes. Much progress has been made since then andthis has been summarised by, for example, Lahmam-Bennani3 for ioniza-tion and Andersen and Bartschat4(and references therein) for excitation.

Parallel theoretical studies have also been made. Indeed the recentwork of Rescigno et al5, claiming a complete solution of the Coulomb3-body problem, has sparked intense debate with respect to ionizationof atomic hydrogen.

In this article we concentrate on recent developments using both ex-perimental techniques to study ionization processes other than thosewhich lead directly to production of the ground state ion. The main ex-amples are double excitation-autoionization and simultaneous ionization-excitation. These processes, involving two active atomic electrons, havebeen the subject of relatively little experimental study using these tech-niques and theoretical approaches have met with only limited success sofax.

1. Double excitation-autoionizationA simple example of this type is:

e(fco) + H e{ls2)lS =• He(2l, 2/')1'3L + e(ks), (1)

the doubly excited state decaying to the ground state ion,

He(2l, 2Z')1'3L =• He+(ls)2S + e(ke). (2)

These doubly excited states are degenerate in energy with continuumstates from the direct ionization process,

e(fco) + He{ls2)lS =• He+(ls)2S + e(ks) + e(ke). (3)

Interference between the two processes occurs, dependent on both themagnitudes and relative phases of the competing direct and resonantamplitudes. These in turn depend on the scattered and ejected electronmomenta and the resonant state symmetry.

The first (e,2e) studies of these autoionizing states were performedby Weigold et al6 and then by Pochat et al7. However, the more recenthigher energy resolution experiments8"14 are of greater value as a testof theoretical models15"18.

Figure 1 shows the measured11 ejected electron energy dependenceof the normalised coincidence signal in the region of the (2p2)xD (35.42eV) and (2s2p)xP (35.56 eV) autoionizing states of helium at an incidentelectron energy of 200 eV and an electron scattering angle 9\ = 12°. The

Correlation studies 15

- £««200cV0. = 12°

% f - • . . - /.<••. /.'

•

• i —iLUPS-ttiIUIPS-D2

*,. MWW-B1\ m\ xrm\"-Ba

\ »

35.0 35.2 35,1 35.6 35*ejected electron energy (eV)

Figure 1. (e,2e) spectra as a function of ejected electron energy in the vicinityof the (2p2)xD and (2S2P)1? autoionizing states of helium at an incident electronenergy of 200 eV and an electron scattering angle 0i = 12°. •, experiment of Croweand McDonald11; RMPS-B1/B2, Fang and Bartschat18; MWW-B1/B2, Marchalantet al17. (from Fang and Bartschat18)

bottom spectrum, showing data at an ejected electron angle 02 = 240° isdominated by the autoionizing states with little or no evidence of inter-ference. On the other hand, the upper spectrum at an ejected electronangle of 50° shows strong interference between the direct ionization andautoionizing channels.

Also shown in figure 1 are the recent calculations of Marchalant etal17 and of Fang and Bartschat18. Both groups used first- and second-order models to predict the spectra. It is clear that for 02 = 240°, bothfirst-order calculations fail to predict the relative intensities of the twostates, while the second-order calculations show a major improvement,supporting the view that a two-step mechanism19'20 must be includedin any realistic description of the process. At 02 = 50°, the agreementbetween theory and experiment is less good. Indeed, the first-ordertheories seem to do better in this case.

From figure 2, which shows the rapid variation of the TDCS as afunction of ejected electron energy, calculated using the second-orderapproach of Fang and Bartschat, it is clear that care has to be takenin comparing theoretical and experimental results. Experimental reso-lution must be accurately accounted for in making comparisons10. Thismay be most important when extracting resonance parameters21'22 fromthe data and may explain why consistent parameters could not be ex-


m

Figure 2. TDCS as a function of ejected electron energy E2 and angle O2 in thevicinity of the (2p2)1D and (2S2P)1? autoionizing states of helium at an incidentelectron energy of 200 eV and an electron scattering angle B\ = 12°, calculated usingthe RMPS-B2 approach of Fang and Bartschat18. (from Fang and Bartschat18)

tracted from the data of and McDonald and Crowe10 for resolutions >80 meV. Although good agreement is obtained between the resonanceparameters for the (2s2)1S, (2p2)xD and (2S2P)1? states measured byLower and Weigold8 and McDonald and Crowe9'10, especially in the for-ward direction, it is clear that more experimental and theoretical workis required to provide a better understanding of these processes.

2. Simultaneous ionization-excitationAs an example we consider the process:

He(ls2)lS =* He+(n = 2) + e(ks) + e(ke). (4)

A number of experimental (e,2e) studies of the dynamics of this pro-cess have been carried out at incident electron energies ranging fromunder twice the threshold energy E^ to 85 E2^~28. Recent examples ofcorresponding theoretical studies include those of Marchalant et al29"31,Kheifets et al32 and Fang and Bartschat33. Figure 3 shows a compari-son between data at incident electron energies of 5.5 keV and scatteringangles < 1 ° and at 645 eV and a scattering angle of 4° for differentejected electron energies, and two recent theoretical calculations.

It is clear that unlike ionization of helium where the ion is left in itsground state, the TDCS for the n = 2 states, particularly at lower ejectedelectron energies, no longer show the two well defined 'binary' and 're-coil' peaks. The additional complexity in this case can be shown29 to


0.100 -

0.050

0.000

* i//Jf/

x l

I

L i

x

0.000

0.002

0.001

0.000

. 0.002

0.000

0.006 -

0.004 -

0.002 -

0.000 , 3^rr..tJ

c / > :

>

CO 120 180 240 300 3C0 0 60 120 180 240 300 360

ejected electron angle (deg)

Figure 3. TDCS for ionization-excitation to the n = 2 states of He*. Experiment:Dupre et al25, Eo « 5500keV and ejected electron energies of 5 eV (a), 10 eV (b), 75eV(c), for scattered electron angles < 1 °; Avaldi et al24, Eo = 645 eV and ejectedelectron energies of 10 eV (a), 40 eV (b), 20 eV(c), for a scattered electron angle of 4°.Theory: Marchalant et al31, second-order two-step (dash-dot); Fang and Bartschat33,second-order RMPS (full curve); first-order RMPS (broken curve), (from Fang andBartschat33 )

arise from the different angular contributions of the unresolved 2s, 2po,istates. Good qualitative agreement is seen between the two second-ordercalculations and the experiments, the level of agreement being generallyworse at the lower ejected electron energies. The very recent RMPS-B2calculations of Fang and Bartschat34 show that both the (A£,4t) au-toionizing states and the experimental resolution can significantly affectcomparisons with these experiments and that of Rouvellou28 when theejected electron energy is close to the energy separation between thesestates and the He+(n = 2) states (« 10 eV).


0.00 60 120 180 240 300 360

Ejected electron angle (deg)

Figure 4. Measured (e,2e) cross sections for the n = 1 - 4 states of He"1" for 200eV electron scattering through 11°. •, Dogan and Crowe27; A, Schlemmer et al35 forn = 1 at 250 eV and a scattering angle of 12°. 6K is the momentum transfer directionin the experiment of Dogan and Crowe and OKI in that of Schlemmer et al.

A recent extension of this work in this laboratory27 to the n = 3,4states of He+ is shown in figure 4. The higher angular momentum statesexcited for n = 3,4 obviously present a major theoretical challenge. Nocalculations are available for the n = 2 — 4 states at 200 eV.

The (e,2e) method has disadvantages, both inherent and in practice,when applied to He+(n = 2). The inability to separate the 2s and 2p


3.5 4.0 4.5 5.0 5.5

6 8 10 12

Ejected electron energy (eV)

Figure 5. Measured DDCS of Dogan et al37 for the He+(2p) state as a function ofejected electron energy. The incident electron energy is 200 eV, the scattering angle5° and the photon detection angle is 130°. The energy resolution is « 1 eV (FWHM).On the right are data at a higher resolution « 0.5 eV(FWHM) in the autoionizationregion compared with a calculation of Balashov (private communication).

ion states has already been mentioned. The TDCS for most kinematicsis more than two orders of magnitude lower than for ground state ion-ization. This not only reduces the n = 2 true coincidence signal relativeto n = 1, but in addition a large random coincidence signal is observeddue to the high number of indistinguishable n = 1 electrons detected.

The electron-photon correlation method enables the 2p ion state tobe isolated and studied in more detail. The decay process is:

He¥{2p)2P =» He+(ls)2S + /n/(30.4nro). (5)

Two groups36'37 have observed this photon in coincidence with a fastscattered electron. The coincidence signal as a function of the energy ofone of the outgoing electrons gives the double differential cross section(DDCS) (slightly distorted due to the different electron-photon angu-lar correlations for different outgoing electron energies) for the He+(2p)state.

Figure 5 shows the experimental data of Dogan et al37 at an inci-dent electron energy of 200 eV and for the fixed electron and photondetector angles shown. The characteristic peak at zero ejected electron


180 0 180

300 300

15.0eV120

300

Figure 6. Measured electron-photon angular correlations of Dogan and Crowe38 forthe He+(2p) state for the three ejected electron energies shown. The incident electronenergy is 200 eV and the scattering angle 5°. The solid lines shown are fits to theexperimental data. The incident electron beam is in the zero direction.

energy, followed by a decrease to higher energies is observed. How-ever, there is also clear structure in the DDCS. The structure at ejectedenergies around 4.3 eV can be associated with interference between di-rect He+(2p) production and indirect production through the (3 ,̂3-T)autoionizing states. The maximum around 8 eV may be due to the in-fluence of higher autoionizing states. Alternatively it lies close to theenergy corresponding to the He+(n = 3) states which cannot be isolatedfrom the He+(2p) signal in these experiments. A kinematically complete(e,2e7) experiment39'40 is required to remove this ambiguity.

Figure 6 shows electron-photon angular correlations measured in thislaboratory at an incident electron energy of 200 eV and a scattering


angle of 5°. The amplitude of the correlation is greatest for the lowestejected electron energy of 1.2 eV and is well reproduced by various Born-R-matrix calculations37. When the ejected electron energy correspondsto the autionization feature at 4.3 eV, an almost isotopic distribution isobserved. However, at an energy of 15.0 eV, the correlation has becomemore anisotropic again, perhaps indicating that indirect processes areless important at this energy. There is also a substantial change in theangular position of the correlation maximum compared with the lowerejected electron energies.

3. SummaryRecent developments, both experimental and theoretical, in the study

of ionization processes involving two active atomic electron processes inthe simplest atom supporting these, helium, are discussed. Considerableprogress has been made in the last few years but further work is requiredbefore the level of agreement between theory and experiment is similarto that for one active electron processes. For ionization-excitation, nocalculations of the TDCS are available for incident electron energiesbelow 366 eV, where some of the most interesting aspects are likely tobe found and experimental data are available.

References1. H. Ehrhardt, M. Schulz, T. Tekaat and K. Willmann, Phys. Rev. Lett. 22, 89

(1969).2. M. Eminyan, K.B. Mac A dam, J. Slevin and H. Kleinpoppen, Phys. Rev. Lett. 31,

576 (1972).3. A. Lahmam-Bennani, J. Phys. B 24, 2401 (1991).4. N. Andersen and K. Bartschat, J. Phys. B 30, 5071 (1997).5. T.N. Rescigno, M. Baertschy, W.A. Isaacs and C.W. McCurdy, Science 286, 2474

(1999).6. E. Weigold, A. Ugbabe and P.J.O. Teubner, Phys. Rev. Lett. 35, 209 (1975).7. A. Pochat, R.J. Tweed, M. Doritch and J. Peresse, J. Phys. B 15, 2269 (1982).8. J. Lower and E. Weigold, J. Phys. B 23, 2819 (1990).9. D.G. McDonald and A. Crowe, Z. Phys. D 23, 371 (1992).10. D.G. McDonald and A. Crowe, J. Phys. B 26, 2887 (1993).11. A. Crowe and D.G. McDonald, in (e,2e) and Related Processes, C.T. Whelan,

H.R.J. Walters, A. Lahmam-Bennani and H. Ehrhardt (eds) (Dordrecht: Kluwer)383 (1993).

12. O. Samardzic, A.S. Kheifets, E. Weigold, B. Shang and M.J. Brunger, J. Phys. B28, 725 (1995).

13. M.J. Brunger, O. Samardzic, A.S. Kheifets and E. Weigold, J. Phys. B 30, 3267(1997).

14. O. Samardzic, L. Campbell, M.J. Brunger, A.S. Kheifets and E. Weigold, J. Phys.B 30, 4383 (1997).

15. A.S. Kheifets, J. Phys. B 26, 2053 (1993).


16. I.E. McCarthy and B. Shang, Phys. Rev. A 47, 4807 (1993).17. P. J. Marchalant, C.T. Whelan and H.R.J. Walters, in Coincidence Studies of

Electron and Photon Impact Ionization, C.T. Whelan and H.R.J. Walters (eds)(New York: Plenum) 21 (1997)

18. Y. Fang and K. Bartschat, J. Phys. B 34, 2747 (2001).19. A.L. Godunov, N.V. Novikov and V.S. Shenashenko, J. Phys. B 24, L173 (1991).20. R.J. Tweed, Z. Phys. D 23, 309 (1992).21. B.W. Shore, Rev. Mod. Phys. 39, 439 (1967).22. V.V. Balashov, S.S. Lipovetskii and V.S. Shenashenko, Sov. Phys.-JETP 36, 858

(1973).23. G.Stefani, L. Avaldi and R. Camilloni, J. Phys. B 23, L227 (1990).24. L. Avaldi, R. Camilloni, R. Multari, G. Stefani, J. Langlois, O. Robaux, R.J.

Tweed and G. Nguyen Vien, J. Phys. B 31, 2981 (1998).25. C. Dupre, A. Lahmam-Bennani, A. Duguet, F. Moto-Furtado, P.F. O'Mahony

and C. Dal Cappello, J. Phys. B 25, 259 (1992).26. A.J. Murray and F.H. Read, J. Phys. B 25, L579 (1992).27. M. Dogan and A. Crowe, J. Phys. B 33, L461 (2000).28. B. Rouvellou, S. Rioual, A. Pochat, R.J. Tweed, J. Langlois, G.N. Vien and O.

Robaux, J. Phys. B 33, L599 (2000).29. P.J. Marchalant, C.T. Whelan and H.R.J. Walters, J. Phys. B 31, 1141 (1998).30. P.J. Marchalant, J. Rasch, C.T. Whelan, D.H. Madison and H.R.J. Walters, J.

Phys. B 32, L705 (1999).31. P.J. Marchalant, B. Rouvellou, J. Rasch, S. Rioual, C.T. Whelan, A. Pochat, D.H.

Madison and H.R.J. Walters, J. Phys. B 33, L749 (2000).32. A.S. Kheifets, I. Bray and K. Bartschat, J. Phys. B 32, L433 (1999).33. Y. Fang and K. Bartschat, J. Phys. B 34, L19 (2001).34. Y. Fang and K. Bartschat, Phys. Rev. A 64, 020701 (2001).35. P. Schlemmer, M.K. Srivastava, T. Rosel and H. Ehrhardt, J. Phys. B 24, 2719

(1991).36. P.A. Hayes and J.F. Williams, Phys. Rev. Lett. 77, 3098 (1996).37. M. Dogan, A. Crowe, K. Bartschat and P.J. Marchalant, J. Phys. B 31, 1611

(1998).38. M. Dogan and A. Crowe, J. Phys. B 35, (to be published)39. V.V. Balashov and I.V. Bodrenko, J. Phys. B 32, L687 (1999).40. M. Dogan, B. Lohmann, D. Cvejanovic and A. Crowe, in XXIIICPEAC Abstracts

of Contributed Papers, S. Datz et al (eds) (Princeton:Rinton) 181 (2001)

COHERENT ELECTRON IMPACT EXCITATIONOF ATOMS

Danica CvejanovicSchuster Laboratory, The University Of Manchester,

Manchester MIS 9PL, UK

[email protected]

Albert Crowe and Derek BrownDepartment of Physics, University of Newcastle,Newcastle upon Tyne NE1 1RU, UK

AbstractExperimental studies of electron impact excitation, of atoms with

closed ns shells are discussed in terms of electron impact coherenceparameters, EICPs. Experimental and theoretical data leading to fulldetermination of complex scattering amplitudes for the S-D excitationin helium and S-P in alkaline earth atoms are presented. Similaritiesand differences in the angular behaviour of EICPs within the alkalineearth group are discussed and compared with helium.

1. IntroductionElectron impact excitation of atoms has been traditionally character-

ized by measurement of differential cross sections, DCS, which are spe-cific for scattering kinematics. More recently, electron impact excitationis characterized in a very detailed way by measurement of Electron Im-pact Coherence Parameters, EICPs. Compared to DCS, EICPs containadditional information on the excitation of magnetic sublevels correlatedto a particular momentum transfer. Measurement of a sufficient num-ber of EICPs can provide complete information on complex scatteringamplitudes, their magnitudes and relative phases. In this sense, such ex-periments are known as "perfect" or "complete" scattering experimentsand parameter sets as complete sets (Bederson, 1969a; Bederson, 1969b).

23

24 Danica Cvejanovil et al.

Generally accepted nowadays is a frame independent set of EICPs,known as Andersen or charge cloud parameters. These present the mosttransparent description of the shape and dynamics of the excited statecharge cloud. However, the charge cloud parameters are not the best setwhen complete information on excitation of higher angular momentumstates is to be achieved. This is the case in the well studied S-D excitationin helium where a new parameterization has been recently introduced (Andersen and Bartschat, 1996; Andersen and Bartschat, 1997).

Being relative, EICPs present an ideal ground for comparison of ex-perimental and theoretical data. In addition, they present the. moststringent test on theoretical modelling. This is especially the case whenoptically forbidden transitions are studied, i.e. transitions where two ormore units of angular momentum are transferred in the collision or whentransitions involving change of spin are studied. An example is excita-tion of the 3D states in helium, where good agreement with experimentshas been observed only after the development of a new generation oftheories, Convergent Close Coupling, CCC, (Fursa and Bray, 1995) andR-matrix with Pseudo States, RMPS (Bartschat, 1999).

In view of the success and significance which a co-ordinated experi-mental and theoretical effort has had in the description of the 3D exci-tation in helium, it seems appropriate that similar studies on excitationof alkaline earth atoms should be a logical continuation. Like helium,alkaline earth atoms have two electrons in a full s shell. The existenceof a closed shell core and electron correlation effects, different from thehelium case, result in additional complexities in theoretical modellingof alkaline earth atoms. These differences should be reflected on mod-elling of the collision dynamics but with increasing atomic mass alongthe group, the structure calculation part as well.

2. Experimental methodsData on excitation of helium are obtained from electron photon coin-

cidence experiments, the majority of them by application of the polar-ization correlation method. Excitation of the alkaline earth atoms hasbeen studied by the polarization correlation method and by superelasticscattering, both of which have been described previously. For examplesof experimental arrangements used for some of the data presented here,i.e. polarization studies on helium and magnesium in Newcastle, seeFursa et al., 1997 and for superelastic scattering on barium, see Li andZetner, 1994 and references therein.

Both methods are based on electron spectrometers with a crossedbeam geometry. The essential geometry in both types of experiment is

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